The data set contains 1989 records. The overall descriptive statistics:

##     Married     Meet credit history guidelines
##  No     : 678   0  : 171                      
##  Unknown:   3   1  :1816                      
##  Yes    :1308   666:   2                      
##                                               
##                                               
##                                               
##  Other obligations as a percent of total income non-Hispanic Black
##  Min.   : 0.00                                  No :1792          
##  1st Qu.:28.00                                  Yes: 197          
##  Median :33.00                                                    
##  Mean   :32.39                                                    
##  3rd Qu.:37.00                                                    
##  Max.   :95.00                                                    
##  Hispanic        Male      Mortgage loan approved
##  No :1878   No     : 369   No : 244              
##  Yes: 111   Unknown:  15   Yes:1745              
##             Yes    :1605                         
##                                                  
##                                                  
##                                                  
##  Loan amount/purchase price                 Race     
##  Min.   :  2.105            Hispanic          : 111  
##  1st Qu.: 70.000            non-Hispanic Black: 197  
##  Median : 80.000            non-Hispanic White:1681  
##  Mean   : 77.064                                     
##  3rd Qu.: 89.894                                     
##  Max.   :257.143

Descriptive statistics by Race:

## $Hispanic
##     MARRIED   GDLIN        OBRAT            MALE    APPROVE 
##  No     :31   0  :16   Min.   :14.60   No     :22   No :26  
##  Unknown: 1   1  :95   1st Qu.:29.00   Unknown: 2   Yes:85  
##  Yes    :79   666: 0   Median :33.00   Yes    :87           
##                        Mean   :33.46                        
##                        3rd Qu.:38.45                        
##                        Max.   :62.00                        
##     LOANPRC                       RACE    
##  Min.   : 39.39   Hispanic          :111  
##  1st Qu.: 80.00   non-Hispanic Black:  0  
##  Median : 89.39   non-Hispanic White:  0  
##  Mean   : 85.17                           
##  3rd Qu.: 90.42                           
##  Max.   :162.63                           
## 
## $`non-Hispanic Black`
##     MARRIED    GDLIN         OBRAT            MALE     APPROVE  
##  No     : 76   0  : 53   Min.   : 5.60   No     : 51   No : 64  
##  Unknown:  0   1  :144   1st Qu.:31.00   Unknown:  2   Yes:133  
##  Yes    :121   666:  0   Median :35.00   Yes    :144            
##                          Mean   :34.94                          
##                          3rd Qu.:38.90                          
##                          Max.   :63.00                          
##     LOANPRC                       RACE    
##  Min.   : 28.99   Hispanic          :  0  
##  1st Qu.: 80.00   non-Hispanic Black:197  
##  Median : 87.02   non-Hispanic White:  0  
##  Mean   : 83.97                           
##  3rd Qu.: 90.24                           
##  Max.   :255.52                           
## 
## $`non-Hispanic White`
##     MARRIED     GDLIN          OBRAT            MALE      APPROVE   
##  No     : 571   0  : 102   Min.   : 0.00   No     : 296   No : 154  
##  Unknown:   2   1  :1577   1st Qu.:27.60   Unknown:  11   Yes:1527  
##  Yes    :1108   666:   2   Median :32.50   Yes    :1374             
##                            Mean   :32.02                            
##                            3rd Qu.:36.50                            
##                            Max.   :95.00                            
##     LOANPRC                        RACE     
##  Min.   :  2.105   Hispanic          :   0  
##  1st Qu.: 68.182   non-Hispanic Black:   0  
##  Median : 79.888   non-Hispanic White:1681  
##  Mean   : 75.719                            
##  3rd Qu.: 89.623                            
##  Max.   :257.143

Descriptive statistics by Marital Status:

## $No
##     MARRIED    GDLIN         OBRAT            MALE     APPROVE  
##  No     :678   0  : 64   Min.   : 4.00   No     :252   No :102  
##  Unknown:  0   1  :614   1st Qu.:28.00   Unknown:  7   Yes:576  
##  Yes    :  0   666:  0   Median :33.00   Yes    :419            
##                          Mean   :32.74                          
##                          3rd Qu.:37.00                          
##                          Max.   :83.00                          
##     LOANPRC                        RACE    
##  Min.   :  2.105   Hispanic          : 31  
##  1st Qu.: 72.426   non-Hispanic Black: 76  
##  Median : 80.000   non-Hispanic White:571  
##  Mean   : 77.967                           
##  3rd Qu.: 89.978                           
##  Max.   :162.626                           
## 
## $Unknown
##     MARRIED  GDLIN       OBRAT           MALE   APPROVE    LOANPRC      
##  No     :0   0  :0   Min.   :13.0   No     :1   No :0   Min.   : 86.96  
##  Unknown:3   1  :3   1st Qu.:23.3   Unknown:0   Yes:3   1st Qu.: 88.62  
##  Yes    :0   666:0   Median :33.6   Yes    :2           Median : 90.29  
##                      Mean   :27.2                       Mean   : 98.16  
##                      3rd Qu.:34.3                       3rd Qu.:103.76  
##                      Max.   :35.0                       Max.   :117.24  
##                  RACE  
##  Hispanic          :1  
##  non-Hispanic Black:0  
##  non-Hispanic White:2  
##                        
##                        
##                        
## 
## $Yes
##     MARRIED     GDLIN          OBRAT            MALE      APPROVE   
##  No     :   0   0  : 107   Min.   : 0.00   No     : 116   No : 142  
##  Unknown:   0   1  :1199   1st Qu.:28.00   Unknown:   8   Yes:1166  
##  Yes    :1308   666:   2   Median :33.00   Yes    :1184             
##                            Mean   :32.22                            
##                            3rd Qu.:37.00                            
##                            Max.   :95.00                            
##     LOANPRC                        RACE     
##  Min.   :  8.772   Hispanic          :  79  
##  1st Qu.: 68.857   non-Hispanic Black: 121  
##  Median : 80.000   non-Hispanic White:1108  
##  Mean   : 76.547                            
##  3rd Qu.: 89.866                            
##  Max.   :257.143

Descriptive statistics by Gender:

## $No
##     MARRIED    GDLIN         OBRAT            MALE     APPROVE  
##  No     :252   0  : 31   Min.   : 6.99   No     :369   No : 50  
##  Unknown:  1   1  :338   1st Qu.:28.00   Unknown:  0   Yes:319  
##  Yes    :116   666:  0   Median :33.00   Yes    :  0            
##                          Mean   :32.64                          
##                          3rd Qu.:37.00                          
##                          Max.   :83.00                          
##     LOANPRC                       RACE    
##  Min.   : 11.01   Hispanic          : 22  
##  1st Qu.: 70.83   non-Hispanic Black: 51  
##  Median : 80.00   non-Hispanic White:296  
##  Mean   : 77.66                           
##  3rd Qu.: 90.00                           
##  Max.   :255.52                           
## 
## $Unknown
##     MARRIED  GDLIN        OBRAT            MALE    APPROVE 
##  No     :7   0  : 0   Min.   :24.00   No     : 0   No : 0  
##  Unknown:0   1  :15   1st Qu.:29.95   Unknown:15   Yes:15  
##  Yes    :8   666: 0   Median :34.50   Yes    : 0           
##                       Mean   :33.33                        
##                       3rd Qu.:37.65                        
##                       Max.   :40.30                        
##     LOANPRC                      RACE   
##  Min.   :39.39   Hispanic          : 2  
##  1st Qu.:74.93   non-Hispanic Black: 2  
##  Median :75.42   non-Hispanic White:11  
##  Mean   :75.59                          
##  3rd Qu.:80.43                          
##  Max.   :92.90                          
## 
## $Yes
##     MARRIED     GDLIN          OBRAT            MALE      APPROVE   
##  No     : 419   0  : 140   Min.   : 0.00   No     :   0   No : 194  
##  Unknown:   2   1  :1463   1st Qu.:28.00   Unknown:   0   Yes:1411  
##  Yes    :1184   666:   2   Median :33.00   Yes    :1605             
##                            Mean   :32.32                            
##                            3rd Qu.:37.00                            
##                            Max.   :95.00                            
##     LOANPRC                        RACE     
##  Min.   :  2.105   Hispanic          :  87  
##  1st Qu.: 69.655   non-Hispanic Black: 144  
##  Median : 80.000   non-Hispanic White:1374  
##  Mean   : 76.942                            
##  3rd Qu.: 89.881                            
##  Max.   :257.143

There are 3 records are missing married (MARRIED) field.

ID MARRIED GDLIN OBRAT BLACK HISPAN MALE APPROVE LOANPRC RACE
356 Unknown 1 35.0 No Yes Yes Yes 86.95652 Hispanic
759 Unknown 1 33.6 No No Yes Yes 90.28571 non-Hispanic White
1392 Unknown 1 13.0 No No No Yes 117.24140 non-Hispanic White

There are 3 records are missing married (GDLIN) field.

ID MARRIED GDLIN OBRAT BLACK HISPAN MALE APPROVE LOANPRC RACE
881 Yes 666 35 No No Yes Yes 75.82939 non-Hispanic White
1229 Yes 666 26 No No Yes Yes 100.00000 non-Hispanic White

There are 15 records are missing gender (MALE) field.

ID MARRIED GDLIN OBRAT BLACK HISPAN MALE APPROVE LOANPRC RACE
1 No 1 34.5 No No Unknown Yes 75.42373 non-Hispanic White
127 No 1 31.6 No No Unknown Yes 80.80000 non-Hispanic White
286 Yes 1 37.3 No No Unknown Yes 80.05337 non-Hispanic White
452 Yes 1 40.1 Yes No Unknown Yes 75.00000 non-Hispanic Black
618 Yes 1 38.5 No No Unknown Yes 92.90323 non-Hispanic White
695 Yes 1 25.0 No No Unknown Yes 64.48276 non-Hispanic White
762 Yes 1 27.6 No No Unknown Yes 75.55556 non-Hispanic White
768 No 1 35.6 No No Unknown Yes 64.74397 non-Hispanic White
833 Yes 1 24.0 No Yes Unknown Yes 79.80769 Hispanic
979 No 1 31.7 No No Unknown Yes 74.86033 non-Hispanic White
1040 No 1 38.0 Yes No Unknown Yes 75.38462 non-Hispanic Black
1070 Yes 1 40.3 No Yes Unknown Yes 39.39394 Hispanic
1092 Yes 1 29.7 No No Unknown Yes 90.10239 non-Hispanic White
1613 No 1 30.2 No No Unknown Yes 90.00000 non-Hispanic White
1924 No 1 35.8 No No Unknown Yes 75.32051 non-Hispanic White 
##                     APPROVE
## RACE                   No  Yes
##   Hispanic             26   85
##   non-Hispanic Black   64  133
##   non-Hispanic White  154 1527

##          APPROVE
## MARRIED     No  Yes
##   No       102  576
##   Unknown    0    3
##   Yes      142 1166

##          APPROVE
## MALE        No  Yes
##   No        50  319
##   Unknown    0   15
##   Yes      194 1411

## , , RACE = Hispanic
## 
##          APPROVE
## MARRIED     No  Yes
##   No         7   24
##   Unknown    0    1
##   Yes       19   60
## 
## , , RACE = non-Hispanic Black
## 
##          APPROVE
## MARRIED     No  Yes
##   No        27   49
##   Unknown    0    0
##   Yes       37   84
## 
## , , RACE = non-Hispanic White
## 
##          APPROVE
## MARRIED     No  Yes
##   No        68  503
##   Unknown    0    2
##   Yes       86 1022

Logistic Regression Full Model

log(p/1-p) = \(b_0 + b_1 * GDLIN + b_2 * OBRAT + b_3 * BLACK + b_4 * HISPAN + b_5 * MALE + b_6 * LOANPRC + b_7 * MARRIED\)

## 
## Call:  glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = "binomial", data = data1)
## 
## Coefficients:
## (Intercept)       GDLIN1        OBRAT       BLACK1      HISPAN1  
##     1.38153      3.71927     -0.03407     -0.81569     -0.90001  
##     LOANPRC     MARRIED1        MALE1  
##    -0.01681      0.47574     -0.05395  
## 
## Degrees of Freedom: 1968 Total (i.e. Null);  1961 Residual
## Null Deviance:       1475 
## Residual Deviance: 959.4     AIC: 975.4

For every one unit change in OBRAT, the log odds of loan approval (versus non loan approval) decreases by 0.0340739.

For every one unit change in LOANPRC, the log odds of loan approval (versus non loan approval) decreases by 0.0168119.

The log odds of loan approval for applicants that meet credit guidelines increases by 3.719269.

The log odds of loan approval for married applicants increases by 0.4757419.

The log odds of loan approval for Black applicants decreases by 0.8156932.

The log odds of loan approval for Hispanic applicants decreases by 0.9000102.

Statistical Tests for Individual Predictors

##            Overall
## GDLIN1   17.126161
## OBRAT     3.305071
## BLACK1    3.396220
## HISPAN1   2.897795
## LOANPRC   3.313389
## MARRIED1  2.477753
## MALE1     0.229981
## Wald test for GDLIN
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = "binomial", data = data1)
## F =  293.3054  on  1  and  1961  df: p= < 0.000000000000000222
## Wald test for OBRAT
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = "binomial", data = data1)
## F =  10.9235  on  1  and  1961  df: p= 0.00096664
## Wald test for BLACK
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = "binomial", data = data1)
## F =  11.53431  on  1  and  1961  df: p= 0.00069686
## Wald test for HISPAN
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = "binomial", data = data1)
## F =  8.397215  on  1  and  1961  df: p= 0.0037997
## Wald test for MALE
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = "binomial", data = data1)
## F =  0.05289126  on  1  and  1961  df: p= 0.81813
## Wald test for LOANPRC
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = "binomial", data = data1)
## F =  10.97855  on  1  and  1961  df: p= 0.00093849
## Wald test for MARRIED
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = "binomial", data = data1)
## F =  6.13926  on  1  and  1961  df: p= 0.013305
##          llh      llhNull           G2     McFadden         r2ML 
## -479.7016510 -737.7148785  516.0264551    0.3497465    0.2305470 
##         r2CU 
##    0.4372079

Logistic Regression Reduced Model 1

## 
## Call:  glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED, family = "binomial", data = data1)
## 
## Coefficients:
## (Intercept)       GDLIN1        OBRAT       BLACK1      HISPAN1  
##     1.34239      3.72139     -0.03410     -0.81143     -0.89733  
##     LOANPRC     MARRIED1  
##    -0.01677      0.46093  
## 
## Degrees of Freedom: 1968 Total (i.e. Null);  1962 Residual
## Null Deviance:       1475 
## Residual Deviance: 959.5     AIC: 973.5
## Wald test for GDLIN
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED, family = "binomial", data = data1)
## F =  294.1283  on  1  and  1962  df: p= < 0.000000000000000222
## Wald test for OBRAT
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED, family = "binomial", data = data1)
## F =  10.93867  on  1  and  1962  df: p= 0.00095878
## Wald test for BLACK
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED, family = "binomial", data = data1)
## F =  11.47424  on  1  and  1962  df: p= 0.00071961
## Wald test for HISPAN
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED, family = "binomial", data = data1)
## F =  8.358631  on  1  and  1962  df: p= 0.0038808
## Wald test for MARRIED
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED, family = "binomial", data = data1)
## F =  6.482227  on  1  and  1962  df: p= 0.010972
## Wald test for LOANPRC
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED, family = "binomial", data = data1)
## F =  10.92337  on  1  and  1962  df: p= 0.00096669

For every one unit change in OBRAT, the log odds of loan approval (versus non loan approval) decreases by 0.0340979.

For every one unit change in LOANPRC, the log odds of loan approval (versus non loan approval) decreases by 0.0167734.

The log odds of loan approval for applicants that meet credit guidelines increase by 3.721387.

The log odds of loan approval for married applicants decreases by 0.4757419.

The log odds of loan approval for non married applicants decreases by NA.

The log odds of loan approval for Black applicants decreases by 0.8114263.

The log odds of loan approval for Hispanic applicants decreases by 0.8973309.

CIs using profiled log-likelihood

##                   2.5 %       97.5 %
## (Intercept)  0.23664368  2.465735226
## GDLIN1       3.30547346  4.157682544
## OBRAT       -0.05434377 -0.013920887
## BLACK1      -1.27292218 -0.332543498
## HISPAN1     -1.48462721 -0.264593691
## LOANPRC     -0.02697832 -0.006937324
## MARRIED1     0.10487116  0.815796783

CIs using standard errors

##                   2.5 %       97.5 %
## (Intercept)  0.23158635  2.453187301
## GDLIN1       3.29609767  4.146676358
## OBRAT       -0.05430447 -0.013891283
## BLACK1      -1.28092587 -0.341926697
## HISPAN1     -1.50565235 -0.289009441
## LOANPRC     -0.02672039 -0.006826433
## MARRIED1     0.10609951  0.815760700

Odds ratios only

## (Intercept)      GDLIN1       OBRAT      BLACK1     HISPAN1     LOANPRC 
##   3.8281698  41.3216682   0.9664769   0.4442240   0.4076563   0.9833665 
##    MARRIED1 
##   1.5855480

Odds ratios and 95% CI

##                     OR      2.5 %     97.5 %
## (Intercept)  3.8281698  1.2669896 11.7721341
## GDLIN1      41.3216682 27.2614457 63.9232116
## OBRAT        0.9664769  0.9471065  0.9861756
## BLACK1       0.4442240  0.2800122  0.7170975
## HISPAN1      0.4076563  0.2265868  0.7675177
## LOANPRC      0.9833665  0.9733823  0.9930867
## MARRIED1     1.5855480  1.1105675  2.2609765

Logistic Regression Reduced Model 2

## 
## Call:  glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC, 
##     family = "binomial", data = data1)
## 
## Coefficients:
## (Intercept)       GDLIN1        OBRAT       BLACK1      HISPAN1  
##     1.66805      3.69461     -0.03512     -0.81768     -0.85828  
##     LOANPRC  
##    -0.01659  
## 
## Degrees of Freedom: 1968 Total (i.e. Null);  1963 Residual
## Null Deviance:       1475 
## Residual Deviance: 965.9     AIC: 977.9
## Wald test for GDLIN
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED, family = "binomial", data = data1)
## F =  294.1283  on  1  and  1962  df: p= < 0.000000000000000222
## Wald test for OBRAT
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED, family = "binomial", data = data1)
## F =  10.93867  on  1  and  1962  df: p= 0.00095878
## Wald test for BLACK
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED, family = "binomial", data = data1)
## F =  11.47424  on  1  and  1962  df: p= 0.00071961
## Wald test for HISPAN
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED, family = "binomial", data = data1)
## F =  8.358631  on  1  and  1962  df: p= 0.0038808
## Wald test for LOANPRC
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED, family = "binomial", data = data1)
## F =  10.92337  on  1  and  1962  df: p= 0.00096669

For every one unit change in OBRAT, the log odds of loan approval (versus non loan approval) decreases by 0.0351171.

For every one unit change in LOANPRC, the log odds of loan approval (versus non loan approval) decreases by 0.0165852.

The log odds of loan approval for applicants that meet credit guidelines increases by 3.6946116.

The log odds of loan approval for Black applicants decreases by 0.8176845.

The log odds of loan approval for Hispanic applicants decreases by 0.8582767.

CIs using profiled log-likelihood

##                   2.5 %       97.5 %
## (Intercept)  0.59360475  2.764561689
## GDLIN1       3.28231679  4.126731408
## OBRAT       -0.05537654 -0.014888611
## BLACK1      -1.27852143 -0.339452086
## HISPAN1     -1.44328269 -0.227316096
## LOANPRC     -0.02676923 -0.006824773

CIs using standard errors

##                   2.5 %       97.5 %
## (Intercept)  0.58607300  2.750024092
## GDLIN1       3.27321875  4.116004514
## OBRAT       -0.05536176 -0.014872430
## BLACK1      -1.28654690 -0.348822144
## HISPAN1     -1.46462838 -0.251925037
## LOANPRC     -0.02649064 -0.006679743

Odds ratios only

## (Intercept)      GDLIN1       OBRAT      BLACK1     HISPAN1     LOANPRC 
##   5.3018115  40.2299456   0.9654924   0.4414526   0.4238919   0.9835516

Odds ratios and 95% CI

##                     OR      2.5 %     97.5 %
## (Intercept)  5.3018115  1.8105031 15.8720816
## GDLIN1      40.2299456 26.6374146 61.9750205
## OBRAT        0.9654924  0.9461288  0.9852217
## BLACK1       0.4414526  0.2784487  0.7121604
## HISPAN1      0.4238919  0.2361513  0.7966689
## LOANPRC      0.9835516  0.9735859  0.9931985

Model comparison

## Analysis of Deviance Table
## 
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED + 
##     MALE
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED
## Model 3: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)  
## 1      1961     959.40                       
## 2      1962     959.46 -1  -0.0531  0.81770  
## 3      1963     965.87 -1  -6.4163  0.01131 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Likelihood ratio test
## 
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED + 
##     MALE
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED
## Model 3: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
##   #Df  LogLik Df  Chisq Pr(>Chisq)  
## 1   8 -479.70                       
## 2   7 -479.73 -1 0.0531    0.81770  
## 3   6 -482.94 -1 6.4163    0.01131 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Probit Regression Full Model

## 
## Call:  glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## 
## Coefficients:
## (Intercept)       GDLIN1        OBRAT       BLACK1      HISPAN1  
##    0.566210     2.142459    -0.016400    -0.425865    -0.463475  
##     LOANPRC     MARRIED1        MALE1  
##   -0.008409     0.237894    -0.033267  
## 
## Degrees of Freedom: 1968 Total (i.e. Null);  1961 Residual
## Null Deviance:       1475 
## Residual Deviance: 958.8     AIC: 974.8

Statistical Tests for Individual Predictors

## Wald test for GDLIN
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F =  312.1492  on  1  and  1961  df: p= < 0.000000000000000222
## Wald test for OBRAT
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F =  9.41885  on  1  and  1961  df: p= 0.0021771
## Wald test for BLACK
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F =  11.25188  on  1  and  1961  df: p= 0.00081057
## Wald test for HISPAN
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F =  8.034928  on  1  and  1961  df: p= 0.0046354
## Wald test for MALE
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F =  0.0795587  on  1  and  1961  df: p= 0.77793
## Wald test for LOANPRC
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F =  10.54337  on  1  and  1961  df: p= 0.0011857
## Wald test for MARRIED
##  in glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED + MALE, family = binomial(link = "probit"), data = data1)
## F =  6.123722  on  1  and  1961  df: p= 0.013422

Probit Regression Reduced Model 1

## 
## Call:  glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + 
##     MARRIED, family = binomial(link = "probit"), data = data1)
## 
## Coefficients:
## (Intercept)       GDLIN1        OBRAT       BLACK1      HISPAN1  
##    0.541687     2.143873    -0.016411    -0.422677    -0.461722  
##     LOANPRC     MARRIED1  
##   -0.008386     0.228926  
## 
## Degrees of Freedom: 1968 Total (i.e. Null);  1962 Residual
## Null Deviance:       1475 
## Residual Deviance: 958.9     AIC: 972.9
##            Overall
## GDLIN1   17.691026
## OBRAT     3.070619
## BLACK1    3.337594
## HISPAN1   2.825314
## LOANPRC   3.239942
## MARRIED1  2.530275
##          llh      llhNull           G2     McFadden         r2ML 
## -479.4603569 -737.7148785  516.5090432    0.3500736    0.2307356 
##         r2CU 
##    0.4375655

Probit Regression Reduced Model 2

## 
## Call:  glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC, 
##     family = binomial(link = "probit"), data = data1)
## 
## Coefficients:
## (Intercept)       GDLIN1        OBRAT       BLACK1      HISPAN1  
##    0.708006     2.135031    -0.017003    -0.426583    -0.438093  
##     LOANPRC  
##   -0.008356  
## 
## Degrees of Freedom: 1968 Total (i.e. Null);  1963 Residual
## Null Deviance:       1475 
## Residual Deviance: 965.3     AIC: 977.3
##           Overall
## GDLIN1  17.692269
## OBRAT    3.183979
## BLACK1   3.379077
## HISPAN1  2.687345
## LOANPRC  3.247739
##          llh      llhNull           G2     McFadden         r2ML 
## -482.6350057 -737.7148785  510.1597458    0.3457703    0.2282510 
##         r2CU 
##    0.4328537

Model comparison

## Analysis of Deviance Table
## 
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED + 
##     MALE
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED
## Model 3: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)  
## 1      1961     958.84                       
## 2      1962     958.92 -1  -0.0799  0.77742  
## 3      1963     965.27 -1  -6.3493  0.01174 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Likelihood ratio test
## 
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED + 
##     MALE
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC + MARRIED
## Model 3: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
##   #Df  LogLik Df  Chisq Pr(>Chisq)  
## 1   8 -479.42                       
## 2   7 -479.46 -1 0.0799    0.77742  
## 3   6 -482.64 -1 6.3493    0.01174 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TBD

##                      GDLIN OBRAT BLACK HISPAN     MARRIED  LOANPRC
## 1 Does not meet guidelines     0     1      0 Not Married 77.06418
## 2 Does not meet guidelines     1     1      0 Not Married 77.06418
## 3 Does not meet guidelines     2     1      0 Not Married 77.06418
## 4 Does not meet guidelines     3     1      0 Not Married 77.06418
## 5 Does not meet guidelines     4     1      0 Not Married 77.06418
## 6 Does not meet guidelines     5     1      0 Not Married 77.06418
##          fit    se.fit residual.scale        UL        LL PredictedProb
## 1 -0.7616686 0.4664814              1 0.5380848 0.1576296     0.3182841
## 2 -0.7957664 0.4585300              1 0.5257154 0.1551869     0.3109318
## 3 -0.8298643 0.4506741              1 0.5133610 0.1527510     0.3036738
## 4 -0.8639622 0.4429189              1 0.5010397 0.1503213     0.2965122
## 5 -0.8980601 0.4352697              1 0.4887690 0.1478973     0.2894493
## 6 -0.9321579 0.4277323              1 0.4765665 0.1454785     0.2824871
##                 RACE
## 1 non-Hispanic Black
## 2 non-Hispanic Black
## 3 non-Hispanic Black
## 4 non-Hispanic Black
## 5 non-Hispanic Black
## 6 non-Hispanic Black

TBD